数理金融
In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential…
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic…
The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the…
We investigate the behaviour of cryptocurrencies using data for bitcoin, ethereum and ripple which account for over 70% of the cryptocurrency market. We demonstrate that $\alpha$-stable distribution is an appropriately sufficient model for…
Discount is the difference between the face value of a bond and its present value. I propose an arbitrage-free dynamic framework for discount models, which provides an alternative to the Heath--Jarrow--Morton framework for forward rates. I…
We have implemented quantum modeling mainly based on Bohmian Mechanics to study time series that contain strong coupling between their events. We firstly propose how compared to normal densities, our target time series seem to be associated…
This study investigates an optimal consumption--investment problem in which the unobserved stock trend is modulated by a hidden Markov chain that represents different economic regimes. In the classical approach, the hidden state is…
In this paper we show how the relaxation techniques can be used to establish the existence of an optimal contract in presence of information asymmetry. The method we illustrate was initially motivated by the problem of designing optimal…
We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the…
We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning…
We present simple general conditions on the acceptance sets under which their induced monetary risk and deviation measures are comonotonic additive. We show that acceptance sets induce comonotonic additive risk measures if and only if the…
We study robust mean-variance optimization in multiperiod portfolio selection by allowing the true probability measure to be inside a Wasserstein ball centered at the empirical probability measure. Given the confidence level, the radius of…
Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…
A money transfer involves a buyer and a seller. A buyer buys goods or services from a seller. The money the buyer decreases is the same as that the seller increases. At each time step, a pair of socially connected agents are selected and…
We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
The Consumer Financial Protection Bureau defines the notion of payoff amount as the amount that has to be payed at a particular time in order to completely pay off the debt, in case the lender intends to pay off the loan early, way before…
Triangle fees are a novel fee structure for AMMs, in which marginal fees are decreasing in a trade's size. That decline is proportional to the movement in the AMM's implied price, i.e. for every basis point the trade moves the ratio of…
We refer to recent inference methodology and formulate a framework for solving the distributionally robust optimization problem, where the true probability measure is inside a Wasserstein ball around the empirical measure and the radius of…
The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in…